Feldman-Cousins Confidence Levels - Toy MC Method

TL;DR

This paper explains the Feldman-Cousins method for constructing confidence regions in particle physics, emphasizing its algorithmic implementation and connection to 1-CL plots, with applications to Gaussian cases.

Contribution

It provides a clearer, more algorithmic explanation of the Feldman-Cousins toy MC method and demonstrates its application to simple Gaussian scenarios.

Findings

Clarified the Feldman-Cousins recipe for toy MC calculations

Connected the method to 1-CL plots for better interpretation

Applied the approach to Gaussian boundary cases

Abstract

In particle physics, the likelihood ratio ordering principle is frequently used to determine confidence regions. This method has statistical properties that are superior to that of other confidence regions. But it often requires intensive computations involving thousands of toy Monte Carlo datasets. The original paper by Feldman and Cousins contains a recipe to perform the toy MC computation. In this note, we explain their recipe in a more algorithmic way, show its connection to 1-CL plots, and apply it to simple Gaussian situations with boundaries.